void XnVPointDenoiser::UpdatePointDenoise(XnPoint3D &ptToChange, const XnPoint3D &ptDontChange)
{
XnV3DVector vDir = XnV3DVector(ptDontChange) - XnV3DVector(ptToChange);
XnFloat fLen = vDir.Normalize();
XnFloat fSoftThreshold = SoftThreshold(fLen, m_fDistanceThreshold);
XnV3DVector vToChange = ptToChange;
XnV3DVector vDontChange = ptDontChange;
if (fSoftThreshold == 0)
{
ptToChange = vToChange*(1-m_fCloseRatio) + vDontChange*m_fCloseRatio;
}
else
{
XnV3DVector vNewPoint = XnV3DVector(ptToChange) + (fSoftThreshold) * vDir;
ptToChange = vToChange*(1-m_fFarRatio) + vNewPoint*m_fFarRatio;
}
} // XnVPointDenoiser::UpdatePointDenoise
int
main( int argc, char* argv[] )
{
El::Environment env( argc, argv );
try
{
const El::Int m = El::Input("--m","height of matrix",100);
const El::Int n = El::Input("--n","width of matrix",200);
// TODO(poulson): Add options for controlling IPM
const El::Int maxIter =
El::Input("--maxIter","maximum # of iter's",500);
const Real lambda = El::Input("--lambda","DS parameter",0.5);
const bool display = El::Input("--display","display matrices?",false);
const bool print = El::Input("--print","print matrices",false);
El::ProcessInput();
El::PrintInputReport();
El::SparseMatrix<Real> A;
El::Matrix<Real> b, xTrue;
El::Identity( A, m, n );
El::Uniform( b, m, 1 );
if( print )
{
El::Print( A, "A" );
El::Print( b, "b" );
}
if( display )
El::Display( A, "A" );
El::lp::affine::Ctrl<Real> affineCtrl;
affineCtrl.mehrotraCtrl.print = true;
El::Matrix<Real> x;
El::Timer timer;
if( El::mpi::Rank() == 0 )
timer.Start();
El::DS( A, b, lambda, x, affineCtrl );
if( El::mpi::Rank() == 0 )
timer.Stop();
if( print )
El::Print( x, "x" );
const El::Int xZeroNorm = El::ZeroNorm( x );
if( El::mpi::Rank() == 0 )
{
El::Output("Dantzig Selector time: ",timer.Total()," secs");
El::Output("|| x ||_0 = ",xZeroNorm);
}
SoftThreshold( x, El::Sqrt(El::limits::Epsilon<Real>()) );
if( print )
El::Print( x, "xThresh" );
const El::Int xZeroNormThresh = El::ZeroNorm( x );
if( El::mpi::Rank() == 0 )
{
El::Output("|| xThresh ||_0 = ",xZeroNormThresh);
}
}
catch( std::exception& e ) { El::ReportException(e); }
return 0;
}
inline void ADMM
( const Matrix<F>& M,
Matrix<F>& L,
Matrix<F>& S,
const RPCACtrl<Base<F>>& ctrl )
{
typedef Base<F> Real;
const Int m = M.Height();
const Int n = M.Width();
// If tau is not specified, then set it to 1/sqrt(max(m,n))
const Base<F> tau =
( ctrl.tau <= Real(0) ? Real(1)/sqrt(Real(Max(m,n))) : ctrl.tau );
if( ctrl.beta <= Real(0) )
LogicError("beta cannot be non-positive");
if( ctrl.tol <= Real(0) )
LogicError("tol cannot be non-positive");
const Base<F> beta = ctrl.beta;
const Base<F> tol = ctrl.tol;
const double startTime = mpi::Time();
Matrix<F> E, Y;
Zeros( Y, m, n );
const Real frobM = FrobeniusNorm( M );
const Real maxM = MaxNorm( M );
if( ctrl.progress )
cout << "|| M ||_F = " << frobM << "\n"
<< "|| M ||_max = " << maxM << endl;
Zeros( L, m, n );
Zeros( S, m, n );
Int numIts = 0;
while( true )
{
++numIts;
// ST_{tau/beta}(M - L + Y/beta)
S = M;
S -= L;
Axpy( F(1)/beta, Y, S );
SoftThreshold( S, tau/beta );
const Int numNonzeros = ZeroNorm( S );
// SVT_{1/beta}(M - S + Y/beta)
L = M;
L -= S;
Axpy( F(1)/beta, Y, L );
Int rank;
if( ctrl.usePivQR )
rank = SVT( L, Real(1)/beta, ctrl.numPivSteps );
else
rank = SVT( L, Real(1)/beta );
// E := M - (L + S)
E = M;
E -= L;
E -= S;
const Real frobE = FrobeniusNorm( E );
if( frobE/frobM <= tol )
{
if( ctrl.progress )
cout << "Converged after " << numIts << " iterations "
<< " with rank=" << rank
<< ", numNonzeros=" << numNonzeros << " and "
<< "|| E ||_F / || M ||_F = " << frobE/frobM
<< ", and " << mpi::Time()-startTime << " total secs"
<< endl;
break;
}
else if( numIts >= ctrl.maxIts )
{
if( ctrl.progress )
cout << "Aborting after " << numIts << " iterations and "
<< mpi::Time()-startTime << " total secs"
<< endl;
break;
}
else
{
if( ctrl.progress )
cout << numIts << ": || E ||_F / || M ||_F = "
<< frobE/frobM << ", rank=" << rank
<< ", numNonzeros=" << numNonzeros
<< ", " << mpi::Time()-startTime << " total secs"
<< endl;
}
// Y := Y + beta E
Axpy( beta, E, Y );
}
}
inline void ALM
( const ElementalMatrix<F>& MPre,
ElementalMatrix<F>& LPre,
ElementalMatrix<F>& SPre,
const RPCACtrl<Base<F>>& ctrl )
{
DistMatrixReadProxy<F,F,MC,MR>
MProx( MPre );
DistMatrixWriteProxy<F,F,MC,MR>
LProx( LPre ),
SProx( SPre );
auto& M = MProx.GetLocked();
auto& L = LProx.Get();
auto& S = SProx.Get();
typedef Base<F> Real;
const Int m = M.Height();
const Int n = M.Width();
const int commRank = mpi::Rank( M.Grid().Comm() );
// If tau is unspecified, set it to 1/sqrt(max(m,n))
const Base<F> tau =
( ctrl.tau <= Real(0) ? Real(1) / sqrt(Real(Max(m,n))) : ctrl.tau );
if( ctrl.tol <= Real(0) )
LogicError("tol cannot be non-positive");
const Base<F> tol = ctrl.tol;
const double startTime = mpi::Time();
DistMatrix<F> Y( M );
NormalizeEntries( Y );
const Real twoNorm = TwoNorm( Y );
const Real maxNorm = MaxNorm( Y );
const Real infNorm = maxNorm / tau;
const Real dualNorm = Max( twoNorm, infNorm );
Y *= F(1)/dualNorm;
// If beta is unspecified, set it to 1 / 2 || sign(M) ||_2
Base<F> beta =
( ctrl.beta <= Real(0) ? Real(1) / (2*twoNorm) : ctrl.beta );
const Real frobM = FrobeniusNorm( M );
const Real maxM = MaxNorm( M );
if( ctrl.progress && commRank == 0 )
cout << "|| M ||_F = " << frobM << "\n"
<< "|| M ||_max = " << maxM << endl;
Zeros( L, m, n );
Zeros( S, m, n );
Int numIts=0, numPrimalIts=0;
DistMatrix<F> LLast( M.Grid() ), SLast( M.Grid() ), E( M.Grid() );
while( true )
{
++numIts;
Int rank, numNonzeros;
while( true )
{
++numPrimalIts;
LLast = L;
SLast = S;
// ST_{tau/beta}(M - L + Y/beta)
S = M;
S -= L;
Axpy( F(1)/beta, Y, S );
SoftThreshold( S, tau/beta );
numNonzeros = ZeroNorm( S );
// SVT_{1/beta}(M - S + Y/beta)
L = M;
L -= S;
Axpy( F(1)/beta, Y, L );
if( ctrl.usePivQR )
rank = SVT( L, Real(1)/beta, ctrl.numPivSteps );
else
rank = SVT( L, Real(1)/beta );
LLast -= L;
SLast -= S;
const Real frobLDiff = FrobeniusNorm( LLast );
const Real frobSDiff = FrobeniusNorm( SLast );
if( frobLDiff/frobM < tol && frobSDiff/frobM < tol )
{
if( ctrl.progress && commRank == 0 )
cout << "Primal loop converged: "
<< mpi::Time()-startTime << " total secs" << endl;
break;
}
else
{
if( ctrl.progress && commRank == 0 )
cout << " " << numPrimalIts
<< ": \n"
<< " || Delta L ||_F / || M ||_F = "
<< frobLDiff/frobM << "\n"
<< " || Delta S ||_F / || M ||_F = "
<< frobSDiff/frobM << "\n"
<< " rank=" << rank
<< ", numNonzeros=" << numNonzeros
<< ", " << mpi::Time()-startTime << " total secs"
<< endl;
}
}
// E := M - (L + S)
E = M;
E -= L;
E -= S;
const Real frobE = FrobeniusNorm( E );
if( frobE/frobM <= tol )
{
if( ctrl.progress && commRank == 0 )
cout << "Converged after " << numIts << " iterations and "
<< numPrimalIts << " primal iterations with rank="
<< rank << ", numNonzeros=" << numNonzeros << " and "
<< "|| E ||_F / || M ||_F = " << frobE/frobM
<< ", " << mpi::Time()-startTime << " total secs"
<< endl;
break;
}
else if( numIts >= ctrl.maxIts )
{
if( ctrl.progress && commRank == 0 )
cout << "Aborting after " << numIts << " iterations and "
<< mpi::Time()-startTime << " total secs" << endl;
break;
}
else
{
if( ctrl.progress && commRank == 0 )
cout << numPrimalIts << ": || E ||_F / || M ||_F = "
<< frobE/frobM << ", rank=" << rank
<< ", numNonzeros=" << numNonzeros << ", "
<< mpi::Time()-startTime << " total secs"
<< endl;
}
// Y := Y + beta E
Axpy( beta, E, Y );
beta *= ctrl.rho;
}
}
inline void ADMM
( const AbstractDistMatrix<F>& MPre, AbstractDistMatrix<F>& LPre,
AbstractDistMatrix<F>& SPre, const RPCACtrl<Base<F>>& ctrl )
{
auto MPtr = ReadProxy<F,MC,MR>( &MPre ); auto& M = *MPtr;
auto LPtr = WriteProxy<F,MC,MR>( &LPre ); auto& L = *LPtr;
auto SPtr = WriteProxy<F,MC,MR>( &SPre ); auto& S = *SPtr;
typedef Base<F> Real;
const Int m = M.Height();
const Int n = M.Width();
const Int commRank = mpi::Rank( M.Grid().Comm() );
// If tau is not specified, then set it to 1/sqrt(max(m,n))
const Base<F> tau =
( ctrl.tau <= Real(0) ? Real(1)/sqrt(Real(Max(m,n))) : ctrl.tau );
if( ctrl.beta <= Real(0) )
LogicError("beta cannot be non-positive");
if( ctrl.tol <= Real(0) )
LogicError("tol cannot be non-positive");
const Base<F> beta = ctrl.beta;
const Base<F> tol = ctrl.tol;
const double startTime = mpi::Time();
DistMatrix<F> E( M.Grid() ), Y( M.Grid() );
Zeros( Y, m, n );
const Real frobM = FrobeniusNorm( M );
const Real maxM = MaxNorm( M );
if( ctrl.progress && commRank == 0 )
cout << "|| M ||_F = " << frobM << "\n"
<< "|| M ||_max = " << maxM << endl;
Zeros( L, m, n );
Zeros( S, m, n );
Int numIts = 0;
while( true )
{
++numIts;
// ST_{tau/beta}(M - L + Y/beta)
S = M;
Axpy( F(-1), L, S );
Axpy( F(1)/beta, Y, S );
SoftThreshold( S, tau/beta );
const Int numNonzeros = ZeroNorm( S );
// SVT_{1/beta}(M - S + Y/beta)
L = M;
Axpy( F(-1), S, L );
Axpy( F(1)/beta, Y, L );
Int rank;
if( ctrl.usePivQR )
rank = SVT( L, Real(1)/beta, ctrl.numPivSteps );
else
rank = SVT( L, Real(1)/beta );
// E := M - (L + S)
E = M;
Axpy( F(-1), L, E );
Axpy( F(-1), S, E );
const Real frobE = FrobeniusNorm( E );
if( frobE/frobM <= tol )
{
if( ctrl.progress && commRank == 0 )
cout << "Converged after " << numIts << " iterations "
<< " with rank=" << rank
<< ", numNonzeros=" << numNonzeros << " and "
<< "|| E ||_F / || M ||_F = " << frobE/frobM
<< ", and " << mpi::Time()-startTime << " total secs"
<< endl;
break;
}
else if( numIts >= ctrl.maxIts )
{
if( ctrl.progress && commRank == 0 )
cout << "Aborting after " << numIts << " iterations and "
<< mpi::Time()-startTime << " total secs"
<< endl;
break;
}
else
{
if( ctrl.progress && commRank == 0 )
cout << numIts << ": || E ||_F / || M ||_F = "
<< frobE/frobM << ", rank=" << rank
<< ", numNonzeros=" << numNonzeros
<< ", " << mpi::Time()-startTime << " total secs"
<< endl;
}
// Y := Y + beta E
Axpy( beta, E, Y );
}
}
int
main( int argc, char* argv[] )
{
El::Environment env( argc, argv );
try
{
const El::Int m = El::Input("--m","height of matrix",100);
const El::Int n = El::Input("--n","width of matrix",200);
const bool useIPM = El::Input("--useIPM","use Interior Point?",true);
// TODO(poulson): Add options for controlling IPM
const El::Int maxIter =
El::Input("--maxIter","maximum # of iter's",500);
const Real rho = El::Input("--rho","augmented Lagrangian param.",1.);
const Real alpha = El::Input("--alpha","over-relaxation",1.2);
const Real absTol = El::Input("--absTol","absolute tolerance",1e-6);
const Real relTol = El::Input("--relTol","relative tolerance",1e-4);
const Real pinvTol = El::Input("--pinvTol","pseudoinv tolerance",0.);
const bool usePinv =
El::Input("--usePinv","Directly compute pinv(A)",true);
const bool progress = El::Input("--progress","print progress?",true);
const bool display = El::Input("--display","display matrices?",false);
const bool print = El::Input("--print","print matrices",false);
El::ProcessInput();
El::PrintInputReport();
El::DistMatrix<Real> A, b, xTrue;
El::Uniform( A, m, n );
El::Uniform( b, m, 1 );
if( print )
{
El::Print( A, "A" );
El::Print( b, "b" );
}
if( display )
El::Display( A, "A" );
const bool sparse = false;
El::BPCtrl<Real> ctrl(sparse);
ctrl.useIPM = useIPM;
ctrl.admmCtrl.rho = rho;
ctrl.admmCtrl.alpha = alpha;
ctrl.admmCtrl.maxIter = maxIter;
ctrl.admmCtrl.absTol = absTol;
ctrl.admmCtrl.relTol = relTol;
ctrl.admmCtrl.usePinv = usePinv;
ctrl.admmCtrl.pinvTol = pinvTol;
ctrl.admmCtrl.progress = progress;
ctrl.lpIPMCtrl.mehrotraCtrl.print = true;
El::DistMatrix<Real> x;
El::Timer timer;
if( El::mpi::Rank() == 0 )
timer.Start();
El::BP( A, b, x, ctrl );
if( El::mpi::Rank() == 0 )
timer.Stop();
if( print )
El::Print( x, "x" );
const El::Int xZeroNorm = El::ZeroNorm( x );
if( El::mpi::Rank() == 0 )
{
El::Output("Basis Pursuit time: ",timer.Total()," secs");
El::Output("|| x ||_0 = ",xZeroNorm);
}
SoftThreshold( x, El::Sqrt(El::limits::Epsilon<Real>()) );
if( print )
El::Print( x, "xThresh" );
const El::Int xZeroNormThresh = El::ZeroNorm( x );
if( El::mpi::Rank() == 0 )
{
El::Output("|| xThresh ||_0 = ",xZeroNormThresh);
}
}
catch( std::exception& e ) { El::ReportException(e); }
return 0;
}
